Express $(4-5i)(-5+5i)$ in the form $a+bi$, where $a$ and $b$ are integers and $i^2 = -1.$
Answer: We simplify, bearing in mind that $i^2 = -1$. We get  \begin{align*}
(4-5i)(-5+5i) &= 4(-5) + 4(5i) -5i(-5) -5i(5i) \\ &= -20 +20i +25i +25 \\ &= \boxed{5 + 45i}.
\end{align*}